Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (inequalities), and express the conditions of the problem mathematically.

Front

What does the inequality b + t < 15 represent in JoAnn's job problem?

Back

It represents the maximum number of hours JoAnn can work as a baby-sitter (b) and tutor (t) combined, which is less than 15 hours.

Front

What does the inequality 3b + 6t > 66 represent in JoAnn's job problem?

Back

It represents the minimum amount of money JoAnn needs to earn per week, which is more than $66 from her baby-sitting (b) and tutoring (t) jobs.

Front

What is the significance of the inequality y ≥ -5x - 3?

Back

This inequality represents a line on a graph where y is greater than or equal to -5x - 3, indicating the region above the line is included in the solution.

Front

In Cole's basketball challenge, what does the inequality x + y < 10 signify?

Back

It signifies that the total number of shots (2-point shots x and 3-point shots y) must be less than 10.

Front

What does the inequality 2x + 3y ≥ 20 mean in Cole's problem?

Back

It means that the total points scored from 2-point shots (2x) and 3-point shots (3y) must be at least 20 points.

Front

In Luka and Dana's cookie problem, what does x + y ≤ 6 represent?

Back

It represents the total number of hours they can spend baking cookies, which cannot exceed 6 hours.

Front

What does the inequality 32x + 20y ≥ 150 indicate in the cookie problem?

Back

It indicates that the total number of cookies baked (32 chocolate chip cookies per hour and 20 snickerdoodle cookies per hour) must be at least 150.

Front

What does the inequality x + y ≤ 300 represent in Carlos's movie theater problem?

Back

It represents the maximum number of tickets sold for adults (x) and children (y) combined, which cannot exceed the theater's seating capacity of 300.